Hi sreedev,
As well as high currents, the darlington driver also allows high voltages to be switched too (up to 50V with the latest TI ULN2803A ICs.) and protects the picaxe from damage from back-emfs (if the motor or relay protection diodes fail for example).
They are simpler, quicker and cheaper than using MOSFETs, although perhaps not quite as elegant.
Regards
Eclectica